The first data on the yield of the lightest nuclear fragments (protons p, deuterons d, and tritons t) with high transverse momenta pT at an angle of 40° in the laboratory reference frame from nuclear targets bombarded by 50-GeV/c protons and 20A-GeV/c carbon nuclei obtained in the SPIN experiment (IHEP, Protvino, Russia) have been reported. It has been shown that the pA and CA data can be described within a common scaling approach, which possibly indicates that the mechanism of formation of high-pT nuclear fragments is common for these reactions.